Time-changed extremal process as a random sup measure
| dc.contributor.author | Lacaux, Céline | |
| dc.contributor.author | Samorodnitsky, Gennady | |
| dc.date.accessioned | 2014-10-09T13:51:16Z | |
| dc.date.available | 2014-10-09T13:51:16Z | |
| dc.date.issued | 2014-10-09 | |
| dc.description.abstract | A functional limit theorem for the partial maxima of a long memory stable sequence produces a limiting process that can be described as a beta-power time change in the classical Fr\'echet extremal process, for beta in a subinterval of the unit interval. Any such power time change in the extremal process for 0<beta<1 produces a process with stationary max-increments. This deceptively simple time change hides the much more delicate structure of the resulting process as a self-affine random sup measure. We uncover this structure and show that in a certain range of the parameters this random measure arises as a limit of the partial maxima of the same long memory stable sequence, but in a different space. These results open a way to construct a whole new class of self-similar Fr\'echet processes with stationary max-increments. | en_US |
| dc.description.sponsorship | ARO grant W911NF-12-10385 and NSA grant H98230-11-1-0154 | en_US |
| dc.identifier.uri | https://hdl.handle.net/1813/37941 | |
| dc.language.iso | en_US | en_US |
| dc.subject | extremal process | en_US |
| dc.subject | random sup measure | en_US |
| dc.subject | heavy tails | en_US |
| dc.subject | stable process | en_US |
| dc.subject | extremal limit theorem | en_US |
| dc.subject | stationary max-increments | en_US |
| dc.subject | self-similar process | en_US |
| dc.title | Time-changed extremal process as a random sup measure | en_US |
| dc.type | preprint | en_US |
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